The use and thus the generation of THz pulses (particularly consisting of only a few optical cycles) having high energy and high field strength comes more and more into the front nowadays especially in the medical, security, nonlinear spectroscopy, particle manipulation and lots of other fields. Here, and from now on, the term ‘THz radiation’ refers to optical radiation in the far infrared domain with its main spectrum being in the frequency range of 0.1-10 THz.
Optical rectification of laser pulses having femtosecond (fs) pulse length in a nonlinear medium (e.g. in crystals having nonlinear optical properties) can be considered rather efficient methods for generating THz pulses having picosecond (ps) pulse length. Typically, ultrashort THz pulses (i.e. having a pulse length of several ps) may be generated by pump pulses in the visible or near infrared domain having pulse lengths of several hundred fs. As it is known, well defined phase matching conditions have to be satisfied for the occurrence of nonlinear phenomena, which in this case means a so-called velocity matching: the group velocity vp;cs of the pump pulse has to be equal to the phase velocity vTHz;f of the generated THz pulse. If these velocities are close to each other in the medium having nonlinear optical properties, i.e. the group refractive index of the nonlinear medium at the frequency of the pumping does not differ by too much from the phase refractive index in the THz domain, this condition can be satisfied relatively easily—as it is known to a person skilled in the art. However, the efficiency of THz radiation generation is greatly affected by the second order nonlinear optical coefficient of the nonlinear medium. There are materials, whose nonlinear optical coefficient has a preferably high value, but due to the high value of the aforementioned refractive index difference, the velocity-matched THz radiation generation is an unsolvable technical problem. Lithium niobate LiNbO3 (LN) is such a material with extraordinary high optical nonlinearity, in which the ratio of said refractive indices is greater than two.
In such cases, preferably the so-called tilted-pulse-front technique may be used (see the scientific publication of Hebling J. et al. entitled “Velocity matching by pulse front tilting for large-area THz-pulse generation” [Optics Express, 2002, vol. 10, issue 21, pages 1161-1166]. This is based on the fact that generation of THz radiation takes place by means of a light pulse in which the pulse front (intensity front) forms a required angle (γ) with the wave front (phase front). As the generated THz beam propagates perpendicularly to the tilted pulse front, as a consequence of the phase matching condition, the projection of the group velocity vector of pumping onto the direction of the propagation direction of the THz radiation has to be equal to the phase velocity of the THz beam, i.e. theνp;cs cos(γ)=νTHz;f relation has to be satisfied.
In a widespread technical implementation of the tilted-pulse-front technique, the pulse front tilt of a beam of the pump source is induced by diffracting said beam on an (mostly reflective) optical grating. Then the diffracted beam is guided through an optical lens or telescope (i.e. an imaging optics) directly into the nonlinear crystal (e.g. LN) to generate THz radiation in such a manner, that the image of the beam spot appearing on the surface of the optical grating is imaged into the crystal by the lens or telescope, wherein the desired THz radiation is generated as a result of the nonlinear phenomena. The pump pulse is guided onto the entry plane of the crystal mostly/preferably perpendicularly, thus in order to minimize reflection losses, the exit plane and the entry plane of the crystal have to be oriented at an angle γ relative to each other, i.e. the optical medium substantially forms an optical prism to ensure a perpendicular exit of the THz beam from the crystal. The magnitude of angle γ is material specific, thus its value is explicitly determined based on the crystal to be used. That is, in particular, in the case of LN said value is γ≈63°.
Nowadays, the tilted-pulse-front technique substantially is a routine method for generating THz radiation, in the last decade, using LN crystal, an increase of about seven magnitudes has been achieved with this technique in the energy of quasi single cycle THz pulses. The pulse front tilting by a diffraction element, and the transformation on imaging optics disposed after the dispersive element is discussed in numerous publications in the literature, for example—without completeness—the work of H. Hirori et al. entitled “Single-cycle terahertz pulses with amplitudes exceeding 1 MV/cm generated by optical rectification in LiNbO(3)” [see Applied Physics Letters, 2011, vol. 98, issue 9, page 3] that uses LN crystal as nonlinear optical medium or the publication of Blanchard et al. entitled “Terahertz pulse generation from bulk GaAs by a tilted-pulse-front excitation at 1.8 μm” [see Applied Physics Letters, 2014, vol. 105, page 241106], which uses gallium-arsenide crystal with plane parallel structure as nonlinear optical medium. A method for THz radiation generation by the tilted-pulse-front technique is further discussed in the European patent no. EP-2,354,841 B1, which discusses a method and device for THz radiation generation based on optical rectification, carried out by a tilted-pulse-front pump pulse, wherein said pump pulse is guided onto a transmissive or reflective grating where it is diffracted and thus its pulse front is tilted, then this pulse is imaged into a suitable nonlinear crystal, e.g. LN crystal, by an imaging optical system.
The imaging errors (e.g. different types of aberrations) of the imaging optics in the case of tilted-pulse-front THz generation arrangements having imaging optics cause distortion of the pump pulses in the nonlinear medium, namely local pulse length widening, which effect increases by the distance from the optical axis. As one of the important factors determining the efficiency of THz radiation generation is the pulse length of the pump pulse, these imaging errors cause a significant efficiency decrease. Due to the limited optical damage threshold of materials, the increase of the pump energy necessarily leads to the increase of the beam diameter. However in the case of large diameter (i.e. wide) pump beams said pulse length widening causes significant decrease in the efficiency of THz radiation generation.
Thus, the imaging optics is disadvantageous from the point of view of tilted pulse front THz generation arrangements comprising it, because it decreases the efficiency of THz radiation generation at large pump energies, and thus it significantly limits the feasibility of large energy THz radiation generation carried out by the tilted-pulse-front technique, and thus the achievable energy of THz radiation generated thereby.
In recent years, study of imaging optics forming substantial parts of the tilted-pulse-front technique has been the object of numerous studies. For example the publication of J. Fülöp et al. entitled “Design of high-energy terahertz sources based on optical rectification” [see Optics Express, 2010, vol. 18, issue 12, pages 12311-12327] discusses a THz radiation generation arrangement, which is based on the combination of an optical grating (as spectral dispersive element) and a special imaging optics (a collecting lens). The essence of the arrangement is that the pulse front tilt satisfying the velocity matching condition required for coupling in the pump pulse into the nonlinear optical medium that is required for the THz radiation generation is achieved in a single step on an optical grating disposed in the propagation path of the pump pulse, i.e. in the light path, before the imaging optics.
Said scientific publication also provides a detailed guide for the optimal construction of an optical imaging arrangement implemented with the lens. Accordingly, efficient THz radiation generation requires that (i) the pulse front tilt in the crystal is as large as required by the velocity matching condition (e.g. about 63° in the case of LN), and (ii) in order to minimize the effect of imaging errors on the efficiency of THz radiation generation, the pump pulse length along the tilted pulse front in the nonlinear optical medium is as close to the transformation-limited value as possible. In order to satisfy this, the image of the beam spot appearing on the optical grating created in the crystal has to contact the tilted-pulse-front surface along the optical axis.
The imaging errors unique for imaging optics and thus the drawbacks of using imagining optics, however, have not been solved completely.
A further widespread method for THz radiation generation is—besides the tilted-pulse-front THz generation arrangements having imaging optics—the so called contact grating arrangement (see the scientific publication of L. Pálfalvi et al. entitled “Novel setups for extremely high power single-cycle terahertz pulse generation by optical rectification” [Applied Physics Letters, 2008, vol. 92, issue 1, pages 171107-171109]). A characteristic feature of these is that pulse front tilt of the pump beam is achieved on a single optical element having angular-dispersion-inducing property formed in the surface of the nonlinear optical medium (e.g. by etching), preferably by a single step of diffraction on a single transmissive optical grating. The period (or line-density) of the optical grating that is necessary for this is determined by the material of the nonlinear crystal and the emission wavelength of the pump source. The primary parameters limiting the size of the pump beam in the contact grating arrangement is the damage threshold of the material and the dimensional constraints of the crystal growing, therefore particularly large energy pumping (i.e. by a wide beam) can be achieved.
In recent years, THz radiation generation by the contact-grating arrangement has become also a subject of numerous scientific publications; thus the optimal design and practical implementations of suitable contact gratings are discussed relatively widely. As a result of said studies, further factors limiting the use of the contact grating arrangement became apparent.
For example, the work of A. Nagashima et al. entitled “Design of Rectangular Transmission Gratings Fabricated in LiNbO3 for High Power Terahertz-Wave Generation” [see Japanese Journal of Applied Physics, 2010, vol. 49, page 122504-1] and the publication of A. Nagashima et al. entitled “Erratum: Design of Rectangular Transmission Gratings Fabricated in LiNbO3 for High-Power Terahertz-Wave Generation” [see Japanese Journal of Applied Physics, 2012, vol. 51, page 119201-1] extensively study the theoretical modeling of the contact grating to be formed in the surface of a LN crystal. Taking a binary grating profile as a basis (see FIG. 1) the diffraction efficiency of the contact grating was optimized as a function of the lattice constant (d2), the filling factor (f=w/d, here w is the profile width) and the profile depth (h). They came to the conclusion that it was practical to use an intermediate material, in particular, fused silica on the air/LN boundary surface in order to improve the efficiency of only 20% achievable with optimal lattice constant (d2=0.42 μm, line-density of 2380/mm) in the case of an air/LN contact grating setup. According to their theoretical calculations, a diffraction efficiency of 90% may be achieved with the air/fused silica/LN contact grating structure at the optimal lattice constant (d2=0.36 μm, line-density of 2777/mm). As the problem of applying silica on the submicron sized structure of the LN surface is not solved nowadays, the technical/practical implementation of the theoretically obtained structure would be quite difficult, if possible at all.
A possible solution for this technical problem is using a refractive index matching liquid (RIML) on the air/LN crystal boundary surface, as suggested in the work of Ollmann Z. et al. entitled “Design of a contact grating setup for mJ-energy THz pulse generation by optical rectification” [see Applied Physics B, 2012, vol. 108, issue 4, pages 821-826]. This publication discusses the details of coupling in and out of an LN crystal in a contact grating arrangement in the case of numerous possible RIML materials, and the effects of dispersion during propagation through the crystal; in particular, a diffraction efficiency of 98% is predicted for a RIML material with a refractive index equivalent to that of e.g. a type BK7 glass comprising a grating with a lattice constant of 0.35 μm (i.e. line-density of 2874/mm).
However, studies regarding the formation of contact-gratings in the surface of nonlinear optical media, and thus particularly of LN crystals, show that the crystal surfaces can only be machined only up to a certain (material dependent) line-density limit. In particular, if the line-density is above this limit, the profile of the created grating becomes blurred. This causes the actual diffraction efficiency of the grating in typical pump beam wavelengths to fall far below the theoretical predictions, because the diffraction efficiency of the grating is very sensitive to the formed grating profile. According to our studies, this limit in the cases of e.g. LN or LiTaO3 (lithium tantalate) is about 2000/mm for pump beam wavelength of 1030 nm. According to our experimental results, the grating geometries with line densities of 2500-3000 l/mm predicting the promising efficiencies described in the aforementioned publications cannot be practically implemented to achieve the theoretically predicted efficiencies with the methods available nowadays (e.g. reactive ion etching, lithographic methods, ablation techniques, etc.).
Accordingly, the THz radiation generation solutions based on a contact grating are not sufficient for high energy THz radiation generation in themselves, because machining difficulties prevent the formation of good quality grating profiles in cases wherein formation of a grating with high line-density would be necessary.
It should be here further noted, that tilted-pulse-front THz generation arrangements comprising imaging optics and contact grating based THz generation arrangements have been extensively studied and compared with each other in literature as independent solutions providing alternative generating schemes mutually excluding each other. In particular, the publication of M. Kunitski et al. entitled “Optimization of single-cycle terahertz generation in LiNbO3 for sub-50 femtosecond pump pulses” [see Optics Express, 2013, vol. 21, issue 6, pages 6826-6836] compare LN crystal based arrangements for THz radiation generation by tilted pulse front pump pulses. The paper discusses four conventional arrangements with optical grating and imaging optics (with lens, refracting telescope, mirror, reflecting telescope), whose efficacy is compared with each other and with a contact grating arrangement on the basis of model calculations. Optical errors of different optical imaging systems are studied and described in great detail. Based on the result of the comparison, a ranking is established among said arrangements, wherein the contact grating arrangement and the conventional arrangement are considered to be mutually exclusive solutions.
By comparing the advantages and disadvantages of tilted-pulse-front techniques, namely the arrangements comprising imaging optics (from now on, conventional arrangements) and the contact grating based arrangements, we have came to the conclusion, that grating profiles obtained by manufacturing methods available nowadays can be made suitable to provide diffraction efficiencies as predicted by theoretical calculations (but only at significantly greater line densities). According to our studies, this requires the tilting of the pulse front of the pump pulses to the extent required by the velocity matching condition in more than one step, as a series of partial pulse front tilts or, putting this another way, as a sum of pulse front tilts created separately from each other. That is, the pump pulses have to be subjected to pulse front tilting (pre-tilting) before their incidence on the contact grating, which may be carried out by e.g. a combination of an angular-dispersive element and an imaging optics used e.g. in conventional techniques. According to our studies, the pulse front tilt of pump pulses required to satisfy the velocity matching condition is preferably achieved by at least two optical elements with angular-dispersion-inducing property spatially separated from each other (in the light path) instead of a single optical element with angular-dispersion-inducing properties.